When you have two radicals multiplied together, you can multiply their radicands (the stuff under the radical sign):
color(white)=sqrt(color(red)3color(blue)xcolor(green)y)*sqrt(color(red)27color(blue)xcolor(green)(y^3))=√3xy⋅√27xy3
=sqrt(color(red)3color(blue)xcolor(green)y*color(red)27color(blue)xcolor(green)(y^3))=√3xy⋅27xy3
=sqrt(color(red)3*color(blue)x*color(green)y*color(red)27*color(blue)x*color(green)(y^3))=√3⋅x⋅y⋅27⋅x⋅y3
=sqrt(color(red)3*color(red)27*color(blue)x*color(blue)x*color(green)y*color(green)(y^3))=√3⋅27⋅x⋅x⋅y⋅y3
=sqrt(color(red)81*color(blue)(x^2)*color(green)(y^4))=√81⋅x2⋅y4
=sqrtcolor(red)81*sqrtcolor(blue)(x^2)*sqrtcolor(green)(y^4)=√81⋅√x2⋅√y4
=color(red)9*sqrtcolor(blue)(x^2)*sqrtcolor(green)(y^4)=9⋅√x2⋅√y4
=color(red)9*color(blue)x*sqrtcolor(green)(y^4)=9⋅x⋅√y4
=color(red)9*color(blue)x*color(green)(y^2)=9⋅x⋅y2
=color(red)9color(blue)xcolor(green)(y^2)=9xy2
That's the simplified expression. Hope this helped!
